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A characterization of tribes with respect to the Łukasiewicz t -norm

Erich Peter Klement, Mirko Navara (1997)

Czechoslovak Mathematical Journal

We give a complete characterization of tribes with respect to the Łukasiewicz t -norm, i. e., of systems of fuzzy sets which are closed with respect to the complement of fuzzy sets and with respect to countably many applications of the Łukasiewicz t -norm. We also characterize all operations with respect to which all such tribes are closed. This generalizes the characterizations obtained so far for other fundamental t -norms, e. g., for the product t -norm.

A non-archimedean Dugundji extension theorem

Jerzy Kąkol, Albert Kubzdela, Wiesƚaw Śliwa (2013)

Czechoslovak Mathematical Journal

We prove a non-archimedean Dugundji extension theorem for the spaces C * ( X , 𝕂 ) of continuous bounded functions on an ultranormal space X with values in a non-archimedean non-trivially valued complete field 𝕂 . Assuming that 𝕂 is discretely valued and Y is a closed subspace of X we show that there exists an isometric linear extender T : C * ( Y , 𝕂 ) C * ( X , 𝕂 ) if X is collectionwise normal or Y is Lindelöf or 𝕂 is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace Y of an ultraregular...

Applications of the p -adic Nevanlinna theory to functional equations

Abdelbaki Boutabaa, Alain Escassut (2000)

Annales de l'institut Fourier

Let K be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. We apply the p -adic Nevanlinna theory to functional equations of the form g = R f , where R K ( x ) , f , g are meromorphic functions in K , or in an “open disk”, g satisfying conditions on the order of its zeros and poles. In various cases we show that f and g must be constant when they are meromorphic in all K , or they must be quotients of bounded functions when they are meromorphic in an “open disk”. In particular,...

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